The grades on a history midterm at Almond are normally distributed with $\mu = 85$ and $\sigma = 4.5$. Luis earned a $90$ on the exam. Find the z-score for Luis's exam grade. Round to two decimal places.
Answer: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Luis's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{90 - {85}}{{4.5}}} $ ${ z \approx 1.11}$ The z-score is $1.11$. In other words, Luis's score was $1.11$ standard deviations above the mean.